I've seen guys turn this around onto the girl. If done in a funny way, you can get away with calling her stupid names like "muffin face" or "puppy pants". You just have to really play up the cutesie factor for her -- play the puppy-dog eyes, and a silly voice.
I use the nickname "nanna" a lot (another word for grandmother) with girls I meet, and back it up by accusing them of doing things like knitting at home and baking cookies (then insisting they bring some along for me).
Proselytiser is right -- don't get caught in it. If it's constantly in the "do something for me" sense, call her out on it. "Oh, I see what you're doing! Your evil mind control isn't going to work any more -- what's in it for me?"